1) Consider an economy with 1, 000 people and two goods, one private and one public. The people all have the same utility function U,(X; G) = X, - 100/G, where X; is the quantity of the private good consumed by person i and G is the quantity of the public good. The price of the private good is 1 and the price of the public good is 10. Each person has a total income of 1,000. a) Find the Pareto efficient amount of G in this economy. b) Find the voluntary contribution (private provision) equilibrium level of the public good in this economy. Is it efficient? 2) There are 2 individuals living in Freaktown. Each individual's demand for police protection is given by P1 =10-2Q and P, =15-Q where Q is measured in hours of patrol time and P; is the price paid for an hour of patrol time3v2q by individual i for i=1,2. Marginal cost of patrol time is given by MC = 5+6Q. Find the efficient level of public good. 3) Assume that the society consists of three individuals, A, B and C. Their demand functions for the number of street lights are represented by: DA = 10-2P, D; = 15-3P, De = 24-6P. Suppose the marginal cost of providing street lights is $8. How many street lights should be provided so that the provision of this good is Pareto efficient? 4) Let Y be a public good, and X be a private good which can be either consumed or used in the production of the public good. There are three households. Each household has an endowment of 100 units of the private good and zero units of the public good. Preferences of the households are given by: u (x]: y) = $1 + 2(y)1/2, u,(x2: y) = x, + 6(y)1/2, u;(X;; y) = x3 + 8(y)1/2. The public good is produced according to the production function y = f(x) = (1/2)x a) What is the marginal cost of Y (in terms of the private good X)? b) Find the set of Pareto-efficient allocations. 5) Suppose 0103 0?) = 10?+ @?In@(ki : y), and p? => and 0 = )?@(?find the egalitarian Pareto optimal allocation (i.e. the one where every one gets the same utility level), and the competitive equilibrium allocation. 6) An economy is made up of two people. The utility functions are Ul(x) = X1X12 and Uz(x) = 2x21 + 2822 - X11 The initial bundles are w1=(1,0) and w2=(0,1) a) Calculate a competitive equilibrium from w. Draw an Edgeworth box diagram to show your answer. Find the set of Pareto optimal points c) Calculate prices p, and p2. a per-unit subsidy s or tax t, and lump sum cash transfers T1 and T, to bring the economy to the allocation y1=(1/3,1/2), yz=(2/3,1/2)